A third of the Cabinet could walk out if Theresa May steers the country towards a no-deal Brexit, former Conservative Sarah Wollaston claimed amid speculation that more MPs could quit.

Both Labour and the Conservatives are braced for further walkouts as the turbulence at Westminster seems set to continue.

Wollaston claimed the Tory party was “destroying itself” as May drifted to the right under pressure from the European Research Group of Brexiteers.

The Health Select Committee chairwoman was one of three Conservatives who walked out yesterday to join eight ex-Labour MPs in the Independent Group (TIG).

“I know that there are many colleagues on my side who will be watching carefully and expecting Theresa May to be certain that she is not going to take us out on a no-deal Brexit,” Wollaston told BBC Radio 4’s Today programme.

“Certainly I think that a third of the Cabinet, I’m pretty clear, would walk if they were looking at a no-deal Brexit.”

Wollaston said “the Tory party has changed, I think it has changed irredeemably”, adding: “I would say the Tory party is destroying itself.”

The Totnes MP joined the new group alongside former minister Anna Soubry and South Cambridgeshire MP Heidi Allen.

Soubry said former prime minister David Cameron made a last-ditch bid to try to stop them quitting.

She told The Times Red Box podcast that Cameron sent them a text saying: “Is it too late to persuade you to stay?”

As attacks on the prime minister from ex-Tory MPs intensified, Soubry accused May of having a personal “problem” with immigration.

Soubry told BBC2’s Newsnight: “The only reason why she will not agree to the single market is because of free movement of people.

“And I think what’s really worried me about Theresa, and she has history in the Home Office that supports this, because I’m an old barrister, I look at the evidence, and I think she’s got a problem with immigration.

“I really, honestly do.”

Asked if she meant it was a personal rather than policy issue for the PM, Soubry said: “Oh yeah, I think she has a thing about immigration and I don’t know where the hell that’s come from.

“Because in a modern Conservative Party, when you again look at the evidence, you know, if we don’t have all these people that come and do all this work in our country, who on earth is going to do it?”

Fellow TIG MP Allen said that around 100 of her former colleagues on the Tory benches shared her frustrations at the direction of the Conservative Party.

Ms Allen told ITV’s Peston: “I’d say a third of the party.”

Ex-education secretary Justine Greening and former attorney general Dominic Grieve both indicated they would leave the party if the government backed a no-deal Brexit.

Greening told Today she was staying in the Conservative Party “for the moment”.

She warned that the Tories would no longer be credible if they simply became “a Brexit party”.

Asked if she would follow her three former colleagues to the Independent Group she said: “It is something that I have considered, but I have reached a different conclusion for the moment.”

But she indicated that if the Tories were taking the country towards a no-deal Brexit she would leave.

“I don’t think I would be able to stay part of a party that was simply a Brexit party that had crashed us out of the European Union,” she said.

Greening said she had “not seen the prime minister recently” despite asking “on multiple occasions”.

The three MPs who quit yesterday said they had not been contacted by the current leadership before their decision, despite the intervention by Cameron.

The prime minister said she was “saddened” by their decision to quit and insisted that under her leadership the Tories were offering “decent, moderate and patriotic politics”.

Former cabinet minister Lord Mandelson said he felt “morally compromised” staying in Labour following anti-Semitic abuse endured by people such as ex-Labour MP Luciana Berger.

He told ITV’s Peston: “Now what is Jeremy Corbyn going to do about this? I mean, this risks growing from a splinter into a cavernous split in our party if he doesn’t take action to stop it.”

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